Floor-half generating function

⌊ n /2 ⌋

has generating function

\sum_{n \geq 1} ⌊ \frac{n}{2} ⌋ x^{n} = \frac{x ^{2}}{( 1 - x ) ^{2} ( 1 + x )} .

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Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 2 / 6A / b / Solution

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